Question

If l and m are intersecting lines, $l\parallel pandm\parallel q$, then which of the following statements is true?

• A. $l$ is parallel to $q$.
• B. $m$ is parallel to $p$.
• C. $p$ and $q$ intersect
• D. $p$ is parallel to $q$.

Answer 1

Answer: (C)

$p$ and $q$ intersect

P II L Q II M

L X M

let's assume that P and Q don't intersect, so,

$P||Q------\left(i\right)$

But $P||L$ and $Q||M----------\left(ii\right)$

Therefore, equating $i$ and $ii,$ we get that,

$L||M$

But we are given that $L$ intersects $M$

Therefore, our assumption is contradicted,

Hence, $P$ intersects $Q$.